Design, Fabrication and Characterization of a Microwave Resonator ...

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5 MeasurementsSiliconSapphiredesign 1 R24 R25designed for uncoupled undercoupled overcoupled5.85 GHz calculated measuredcoupling capacitance (C uc = 1.2 fF) (C oc =7.1 fF)resonance 4 K 6.003 6.003 6.003 6.151frequency (GHz) 50 mK 6.004 6.004 6.003 –quality factor4 K 5.6 ·10 3 5.6 ·10 3 5.2 ·10 3 1.1 ·10 450 mK 1.6 ·10 4 1.6 ·10 4 1.3 ·10 4 –coupling capacitance (C uc = 1.1 fF) (C oc =6.2 fF)resonance 4 K 6.403 6.403 6.402 6.210frequency (GHz) 50 mK 6.404 6.404 6.403 –quality factor4 K 8.2 ·10 3 8.2 ·10 3 7.5 ·10 3 8 ·10 250 mK 8.3 ·10 10 3.2 ·10 7 8.9 ·10 4 –Table 5.13: Calculated and measured resonance frequencies and quality factors for R24 andR25.SiliconSapphiredesign 1 R26 R27designed for uncoupled undercoupled overcoupled6.00 GHz calculated measuredcoupling capacitance (C uc = 1.2 fF) (C oc =7.1 fF)resonance 4 K 6.157 6.157 6.156 6.337frequency (GHz) 50 mK 6.158 6.158 6.157 –quality factor4 K 5.5 ·10 3 5.5 ·10 3 5.1 ·10 3 0.9 ·10 350 mK 1.6 ·10 4 1.6 ·10 4 1.3 ·10 4 –coupling capacitance (C uc = 1.1 fF) (C oc =6.2 fF)resonance 4 K 6.568 6.567 6.567 –frequency (GHz) 50 mK 6.568 6.568 6.567 –quality factor4 K 8.0 ·10 3 8.0 ·10 3 7.3 ·10 3 –50 mK 8.3 ·10 10 3.2 ·10 7 8.9 ·10 4 –Table 5.14: Calculated and measured resonance frequencies and quality factors for R26 andR27.Sapphiredesign 2R36designed for uncoupled slightly overcoupled5.85 GHz calculated measuredcoupling capacitance(C uc = 31 fF)resonance 4 K 6.39 6.38 5.71frequency (GHz) 50 mK 6.39 6.38 –quality factor4 K 1.8 ·10 4 1.2 ·10 4 3.0 ·10 250 mK 9.6 ·10 10 4.0 ·10 4 –Table 5.15: Calculated and measured resonance frequencies and quality factors for R36 onSapphire.60
6 SimulationsThis chapter gives a brief overview of the simulations done to predict the experimental results.For the simulations done at the Walther-Meißner-Institut the software Sonnet Lite wasused. Additional calculations for the resonator R21 were done at the Institute of Nanoelectronics.6.1 Simulations in SonnetFigure 6.1: Structure in the gold plated box withtwo-ports as simulated in SonnetIt is possible to include superconductivityin the simulations done with Sonnetby using the temperate and frequencydependent inductance derived in (2.26)on page 17. In the simulation processthis inductance is multiplied with the frequency1 . All simulations were performedfor three different regimes, first Niobiumas perfect conductor (labeled as nc), secondat temperatures of 4 K and third at a temperature of 50 mK. The results in the superconductingregime do not vary much with temperature, therefore, both results are summarizedin the superconducting (sc) results.The following parameters were used in the simulations:4 K 50 mKλ L 47.9 nm 47 nmL s 0.060 pH 0.059 pHTable 6.1: Inductance inserted in Sonnet to simulate superconductivity.In the simulations we took advantage of the high symmetry of the resonator structure: Asymmetry axis was laid in the middle of the center strip and Sonnet simulated only one halfof the structure, extrapolating the second half. Thus the computer needed less memory andthe necessary calculation time is reduced by a factor of 7. This procedure has been verifiedby comparing it to a simulation of the whole structure.1 See Sonnet manual page 70ff61
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Contents5.2.3 R27 on Silicon . . .
Page 6 and 7:
1 Motivation and Outlinethe antinod
Page 8 and 9:
2 Theoretical Description of a CPW
Page 10 and 11:
Page 12 and 13:
Page 14: 2 Theoretical Description of a CPW
Page 19 and 20: 2.2 Including Superconductivity in
Page 21 and 22: 2.2 Including Superconductivity in
Page 23 and 24: 2.3 Microwave Resonators2.3.2 Quali
Page 25 and 26: 2.3 Microwave ResonatorsFigure 2.11
Page 27 and 28: 2.3 Microwave ResonatorsFigure 2.13
Page 29 and 30: 2.4 The Scattering MatrixThe first
Page 31 and 32: 3 Designs Procedure for the Resonat
Page 33 and 34: 3.3 ConnectorsFigure 3.1: Coupling
Page 35 and 36: 4 Fabrication and Measurement Setup
Page 37 and 38: 4.2 Measurement SetupDevelop Resist
Page 39 and 40: 4.2 Measurement SetupFigure 4.3: Me
Page 41 and 42: 4.3 Calibration4.3 CalibrationIn or
Page 43 and 44: 5 MeasurementsThe first part of thi
Page 45 and 46: 5.1 First Experimentsname design W
Page 47 and 48: 5.2 Measurements - Design 1Figure 5
Page 49 and 50: 5.2 Measurements - Design 1The adva
Page 51 and 52: 5.2 Measurements - Design 15.2.2 R2
Page 53 and 54: 5.2 Measurements - Design 1Figure 5
Page 55 and 56: 5.3 Measurements - Yale DesignFigur
Page 57 and 58: 5.3 Measurements - Yale DesignFigur
Page 59 and 60: 5.4 Measurement - Design 2: R36 on
Page 61 and 62: 5.5 Discussion of the Experimental
Page 63: 5.5 Discussion of the Experimental
Page 67 and 68: 6.1 Simulations in SonnetFigure 6.4
Page 69 and 70: 6.1 Simulations in SonnetFigure 6.5
Page 71 and 72: 6.2 Simulations Done at the Institu
Page 73 and 74: 7 Conclusion and OutlookThree centr
Page 75 and 76: A Specimen OverviewDesigns for Rose
Page 77 and 78: B Masks73
Page 79 and 80: B.2 Mask for Probing StationB.2 Mas
Page 81 and 82: Bibliography[1] INFORMATIK: Quanten
Page 83 and 84: List of Figures2.1 Different realiz
Page 85 and 86: List of Figures6.6 Forward and back
Page 87 and 88: List of Tables2.1 Values where (2.1
Page 89: DanksagungVor allem möchte ich mic
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